{"product_id":"probabilistic-reliability-models-hardback-9781118341834","title":"Probabilistic Reliability Models (Hardback) 9781118341834","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eProbabilistic Reliability Models\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eIgor A. Ushakov (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781118341834, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 6 November 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e248 pages\u003cbr\u003e23.6 x 15.8 x 2 cm, 0.544 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003ePractical Approaches to Reliability Theory in Cutting-Edge Applications\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eProbabilistic Reliability Models\u003c\/i\u003e helps readers understand and properly use statistical methods\u003c\/p\u003e \u003cp\u003eand optimal resource allocation to solve engineering problems.\u003c\/p\u003e \u003cp\u003eThe author supplies engineers with a deeper understanding of mathematical models while also\u003c\/p\u003e \u003cp\u003eequipping mathematically oriented readers with a fundamental knowledge of the engineeringrelated\u003c\/p\u003e \u003cp\u003eapplications at the center of model building. The book showcases the use of probability\u003c\/p\u003e \u003cp\u003etheory and mathematical statistics to solve common, real-world reliability problems. Following\u003c\/p\u003e \u003cp\u003ean introduction to the topic, subsequent chapters explore key systems and models including:\u003c\/p\u003e \u003cp\u003e• Unrecoverable objects and recoverable systems\u003c\/p\u003e \u003cp\u003e• Methods of direct enumeration\u003c\/p\u003e \u003cp\u003e• Markov models and heuristic models\u003c\/p\u003e \u003cp\u003e• Performance effectiveness\u003c\/p\u003e \u003cp\u003e• Time redundancy\u003c\/p\u003e \u003cp\u003e• System survivability\u003c\/p\u003e \u003cp\u003e• Aging units and their related systems\u003c\/p\u003e \u003cp\u003e• Multistate systems\u003c\/p\u003e \u003cp\u003eDetailed case studies illustrate the relevance of the discussed methods to real-world technical\u003c\/p\u003e \u003cp\u003eprojects including software failure avalanches, gas pipelines with underground storage, and\u003c\/p\u003e \u003cp\u003eintercontinental ballistic missile (ICBM) control systems. Numerical examples and detailed\u003c\/p\u003e \u003cp\u003eexplanations accompany each topic, and exercises throughout allow readers to test their\u003c\/p\u003e \u003cp\u003ecomprehension of the presented material.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eProbabilistic Reliability Models\u003c\/i\u003e is an excellent book for statistics, engineering, and operations\u003c\/p\u003e \u003cp\u003eresearch courses on applied probability at the upper-undergraduate and graduate levels. The\u003c\/p\u003e \u003cp\u003ebook is also a valuable reference for professionals and researchers working in industry who\u003c\/p\u003e \u003cp\u003ewould like a mathematical review of reliability models and the relevant applications.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface xiii  \u003cp\u003eAcronyms and Notations xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 What Is Reliability? 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Reliability as a Property of Technical Objects, 1\u003c\/p\u003e \u003cp\u003e1.2 Other “Ilities”, 2\u003c\/p\u003e \u003cp\u003e1.3 Hierarchical Levels of Analyzed Objects, 5\u003c\/p\u003e \u003cp\u003e1.4 How Can Reliability Be Measured?, 5\u003c\/p\u003e \u003cp\u003e1.5 Software Reliability, 7\u003c\/p\u003e \u003cp\u003e1.5.1 Case Study: Avalanche of Software Failures, 8\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Unrecoverable Objects 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Unit, 9\u003c\/p\u003e \u003cp\u003e2.1.1 Probability of Failure-Free Operation, 9\u003c\/p\u003e \u003cp\u003e2.1.2 Mean Time to Failure, 10\u003c\/p\u003e \u003cp\u003e2.2 Series Systems, 11\u003c\/p\u003e \u003cp\u003e2.2.1 Probability of Failure-Free Operation, 11\u003c\/p\u003e \u003cp\u003e2.2.2 Mean Time to Failure, 13\u003c\/p\u003e \u003cp\u003e2.3 Parallel System, 14\u003c\/p\u003e \u003cp\u003e2.3.1 Probability of Failure-Free Operation, 14\u003c\/p\u003e \u003cp\u003e2.3.2 Mean Time to Failure, 18\u003c\/p\u003e \u003cp\u003e2.4 Structure of Type “k-out-of-n”, 20\u003c\/p\u003e \u003cp\u003e2.5 Realistic Models of Loaded Redundancy, 22\u003c\/p\u003e \u003cp\u003e2.5.1 Unreliable Switching Process, 23\u003c\/p\u003e \u003cp\u003e2.5.2 Non-Instant Switching, 23\u003c\/p\u003e \u003cp\u003e2.5.3 Unreliable Switch, 24\u003c\/p\u003e \u003cp\u003e2.5.4 Switch Serving as Interface, 25\u003c\/p\u003e \u003cp\u003e2.5.5 Incomplete Monitoring of the Operating Unit, 26\u003c\/p\u003e \u003cp\u003e2.5.6 Periodical Monitoring of the Operating Unit, 28\u003c\/p\u003e \u003cp\u003e2.6 Reducible Structures, 28\u003c\/p\u003e \u003cp\u003e2.6.1 Parallel-Series and Series-Parallel Structures, 28\u003c\/p\u003e \u003cp\u003e2.6.2 General Case of Reducible Structures, 29\u003c\/p\u003e \u003cp\u003e2.7 Standby Redundancy, 30\u003c\/p\u003e \u003cp\u003e2.7.1 Simple Redundant Group, 30\u003c\/p\u003e \u003cp\u003e2.7.2 Standby Redundancy of Type “k-out-of-n”, 33\u003c\/p\u003e \u003cp\u003e2.8 Realistic Models of Unloaded Redundancy, 34\u003c\/p\u003e \u003cp\u003e2.8.1 Unreliable Switching Process, 34\u003c\/p\u003e \u003cp\u003e2.8.2 Non-Instant Switching, 35\u003c\/p\u003e \u003cp\u003e2.8.3 Unreliable Switch, 35\u003c\/p\u003e \u003cp\u003e2.8.4 Switch Serving as Interface, 37\u003c\/p\u003e \u003cp\u003e2.8.5 Incomplete Monitoring of the Operating Unit, 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Recoverable Systems: Markov Models 40\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Unit, 40\u003c\/p\u003e \u003cp\u003e3.1.1 Markov Model, 41\u003c\/p\u003e \u003cp\u003e3.2 Series System, 47\u003c\/p\u003e \u003cp\u003e3.2.1 Turning Off System During Recovery, 47\u003c\/p\u003e \u003cp\u003e3.2.2 System in Operating State During Recovery: Unrestricted Repair, 49\u003c\/p\u003e \u003cp\u003e3.2.3 System in Operating State During Recovery: Restricted Repair, 51\u003c\/p\u003e \u003cp\u003e3.3 Dubbed System, 53\u003c\/p\u003e \u003cp\u003e3.3.1 General Description, 53\u003c\/p\u003e \u003cp\u003e3.3.2 Nonstationary Availability Coefficient, 54\u003c\/p\u003e \u003cp\u003e3.3.3 Stationary Availability Coefficient, 58\u003c\/p\u003e \u003cp\u003e3.3.4 Probability of Failure-Free Operation, 59\u003c\/p\u003e \u003cp\u003e3.3.5 Stationary Coefficient of Interval Availability, 62\u003c\/p\u003e \u003cp\u003e3.3.6 Mean Time to Failure, 63\u003c\/p\u003e \u003cp\u003e3.3.7 Mean Time Between Failures, 63\u003c\/p\u003e \u003cp\u003e3.3.8 Mean Recovery Time, 65\u003c\/p\u003e \u003cp\u003e3.4 Parallel Systems, 65\u003c\/p\u003e \u003cp\u003e3.5 Structures of Type “m-out-of-n”, 66\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Recoverable Systems: Heuristic Models 72\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Preliminary Notes, 72\u003c\/p\u003e \u003cp\u003e4.2 Poisson Process, 75\u003c\/p\u003e \u003cp\u003e4.3 Procedures over Poisson Processes, 78\u003c\/p\u003e \u003cp\u003e4.3.1 Thinning Procedure, 78\u003c\/p\u003e \u003cp\u003e4.3.2 Superposition Procedure, 80\u003c\/p\u003e \u003cp\u003e4.4 Asymptotic Thinning Procedure over Stochastic Point Process, 80\u003c\/p\u003e \u003cp\u003e4.5 Asymptotic Superposition of Stochastic Point Processes, 82\u003c\/p\u003e \u003cp\u003e4.6 Intersection of Flows of Narrow Impulses, 84\u003c\/p\u003e \u003cp\u003e4.7 Heuristic Method for Reliability Analysis of Series Recoverable Systems, 87\u003c\/p\u003e \u003cp\u003e4.8 Heuristic Method for Reliability Analysis of Parallel Recoverable Systems, 87\u003c\/p\u003e \u003cp\u003e4.8.1 Influence of Unreliable Switching Procedure, 88\u003c\/p\u003e \u003cp\u003e4.8.2 Influence of Switch’s Unreliability, 89\u003c\/p\u003e \u003cp\u003e4.8.3 Periodical Monitoring of the Operating Unit, 90\u003c\/p\u003e \u003cp\u003e4.8.4 Partial Monitoring of the Operating Unit, 91\u003c\/p\u003e \u003cp\u003e4.9 Brief Historical Overview and Related Sources, 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Time Redundancy 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 System with Possibility of Restarting Operation, 95\u003c\/p\u003e \u003cp\u003e5.2 Systems with “Admissibly Short Failures”, 98\u003c\/p\u003e \u003cp\u003e5.3 Systems with Time Accumulation, 99\u003c\/p\u003e \u003cp\u003e5.4 Case Study: Gas Pipeline with an Underground Storage, 100\u003c\/p\u003e \u003cp\u003e5.5 Brief Historical Overview and Related Sources, 102\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 “Aging” Units and Systems of “Aging” Units 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Chebyshev Bound, 103\u003c\/p\u003e \u003cp\u003e6.2 “Aging” Unit, 104\u003c\/p\u003e \u003cp\u003e6.3 Bounds for Probability of Failure-Free Operations, 105\u003c\/p\u003e \u003cp\u003e6.4 Series System Consisting of “Aging” Units, 108\u003c\/p\u003e \u003cp\u003e6.4.1 Preliminary Lemma, 108\u003c\/p\u003e \u003cp\u003e6.5 Series System, 110\u003c\/p\u003e \u003cp\u003e6.5.1 Probability of Failure-Free Operation, 110\u003c\/p\u003e \u003cp\u003e6.5.2 Mean Time to Failure of a Series System, 112\u003c\/p\u003e \u003cp\u003e6.6 Parallel System, 114\u003c\/p\u003e \u003cp\u003e6.6.1 Probability of Failure-Free Operation, 114\u003c\/p\u003e \u003cp\u003e6.6.2 Mean Time to Failure, 117\u003c\/p\u003e \u003cp\u003e6.7 Bounds for the Coefficient of Operational Availability, 119\u003c\/p\u003e \u003cp\u003e6.8 Brief Historical Overview and Related Sources, 121\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Two-Pole Networks 123\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 General Comments, 123\u003c\/p\u003e \u003cp\u003e7.1.1 Method of Direct Enumeration, 125\u003c\/p\u003e \u003cp\u003e7.2 Method of Boolean Function Decomposition, 127\u003c\/p\u003e \u003cp\u003e7.3 Method of Paths and Cuts, 130\u003c\/p\u003e \u003cp\u003e7.3.1 Esary–Proschan Bounds, 130\u003c\/p\u003e \u003cp\u003e7.3.2 “Improvements” of Esary–Proschan Bounds, 133\u003c\/p\u003e \u003cp\u003e7.3.3 Litvak–Ushakov Bounds, 135\u003c\/p\u003e \u003cp\u003e7.3.4 Comparison of the Two Methods, 139\u003c\/p\u003e \u003cp\u003e7.4 Brief Historical Overview and Related Sources, 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Performance Effectiveness 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Effectiveness Concepts, 143\u003c\/p\u003e \u003cp\u003e8.2 General Idea of Effectiveness Evaluation, 145\u003c\/p\u003e \u003cp\u003e8.2.1 Conditional Case Study: Airport Traffic Control System, 147\u003c\/p\u003e \u003cp\u003e8.3 Additive Type of System Units’ Outcomes, 150\u003c\/p\u003e \u003cp\u003e8.4 Case Study: ICBM Control System, 151\u003c\/p\u003e \u003cp\u003e8.5 Systems with Intersecting Zones of Action, 153\u003c\/p\u003e \u003cp\u003e8.6 Practical Recommendation, 158\u003c\/p\u003e \u003cp\u003e8.7 Brief Historical Overview and Related Sources, 160\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 System Survivability 162\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Illustrative Example, 166\u003c\/p\u003e \u003cp\u003e9.2 Brief Historical Overview and Related Sources, 167\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Multistate Systems 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Preliminary Notes, 169\u003c\/p\u003e \u003cp\u003e10.2 Generating Function, 169\u003c\/p\u003e \u003cp\u003e10.3 Universal Generating Function, 172\u003c\/p\u003e \u003cp\u003e10.4 Multistate Series System, 174\u003c\/p\u003e \u003cp\u003e10.4.1 Series Connection of Piping Runs, 174\u003c\/p\u003e \u003cp\u003e10.4.2 Series Connection of Resistors, 177\u003c\/p\u003e \u003cp\u003e10.4.3 Series Connections of Capacitors, 179\u003c\/p\u003e \u003cp\u003e10.5 Multistate Parallel System, 181\u003c\/p\u003e \u003cp\u003e10.5.1 Parallel Connection of Piping Runs, 181\u003c\/p\u003e \u003cp\u003e10.5.2 Parallel Connection of Resistors, 182\u003c\/p\u003e \u003cp\u003e10.5.3 Parallel Connections of Capacitors, 182\u003c\/p\u003e \u003cp\u003e10.6 Reducible Systems, 183\u003c\/p\u003e \u003cp\u003e10.7 Conclusion, 190\u003c\/p\u003e \u003cp\u003e10.8 Brief Historical Overview and Related Sources, 190\u003c\/p\u003e \u003cp\u003eAppendix A Main Distributions Related to Reliability Theory 195\u003c\/p\u003e \u003cp\u003eA.1 Discrete Distributions, 195\u003c\/p\u003e \u003cp\u003eA.1.1 Degenerate Distribution, 195\u003c\/p\u003e \u003cp\u003eA.1.2 Bernoulli Distribution, 196\u003c\/p\u003e \u003cp\u003eA.1.3 Binomial Distribution, 197\u003c\/p\u003e \u003cp\u003eA.1.4 Poisson Distribution, 198\u003c\/p\u003e \u003cp\u003eA.1.5 Geometric Distribution, 200\u003c\/p\u003e \u003cp\u003eA.2 Continuous Distributions, 201\u003c\/p\u003e \u003cp\u003eA.2.1 Intensity Function, 201\u003c\/p\u003e \u003cp\u003eA.2.2 Continuous Uniform Distribution, 202\u003c\/p\u003e \u003cp\u003eA.2.3 Exponential Distribution, 203\u003c\/p\u003e \u003cp\u003eA.2.4 Erlang Distribution, 204\u003c\/p\u003e \u003cp\u003eA.2.5 Hyperexponential Distribution, 205\u003c\/p\u003e \u003cp\u003eA.2.6 Normal Distribution, 207\u003c\/p\u003e \u003cp\u003eA.2.7Weibull–Gnedenko Distribution, 207\u003c\/p\u003e \u003cp\u003eAppendix B Laplace Transformation 209\u003c\/p\u003e \u003cp\u003eAppendix C Markov Processes 214\u003c\/p\u003e \u003cp\u003eC.1 General Markov Process, 214\u003c\/p\u003e \u003cp\u003eC.1.1 Nonstationary Availability Coefficient, 216\u003c\/p\u003e \u003cp\u003eC.1.2 Probability of Failure-Free Operation, 218\u003c\/p\u003e \u003cp\u003eC.1.3 Stationary Availability Coefficient, 220\u003c\/p\u003e \u003cp\u003eC.1.4 Mean Time to Failure and Mean Time Between Failures, 221\u003c\/p\u003e \u003cp\u003eC.1.5 Mean Recovery Time, 222\u003c\/p\u003e \u003cp\u003eC.2 Birth–Death Process, 223\u003c\/p\u003e \u003cp\u003eAppendix D General Bibliography 227\u003c\/p\u003e \u003cp\u003eIndex 231\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52417766392088,"sku":"9781118341834","price":66.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781118341834.jpg?v=1784507599","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/probabilistic-reliability-models-hardback-9781118341834","provider":"Freshly Printed Books","version":"1.0","type":"link"}